TY - GEN
T1 - Approximability of the independent feedback vertex set problem for bipartite graphs
AU - Tamura, Yuma
AU - Ito, Takehiro
AU - Zhou, Xiao
N1 - Funding Information:
T. Ito?Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. X. Zhou?Partially supported by JSPS KAKENHI Grant Number JP19K11813, Japan.
Funding Information:
T. Ito—Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. X. Zhou—Partially supported by JSPS KAKENHI Grant Number JP19K11813, Japan.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.
PY - 2020
Y1 - 2020
N2 - Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.
AB - Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.
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U2 - 10.1007/978-3-030-39881-1_24
DO - 10.1007/978-3-030-39881-1_24
M3 - Conference contribution
AN - SCOPUS:85080901203
SN - 9783030398804
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 286
EP - 295
BT - WALCOM
A2 - Rahman, M. Sohel
A2 - Sadakane, Kunihiko
A2 - Sung, Wing-Kin
PB - Springer
T2 - 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
Y2 - 31 March 2020 through 2 April 2020
ER -